Method for designing a lens shape and spectacle lens

Abstract

A computer-implemented method for providing a lens shape for an ophthalmic lens is disclosed. Further, there is provided a method for angular smoothing of a surface determined by carrier lines radially outwards of a prescription zone bordered by a first boundary line. In addition, there is provided an ophthalmic lens, in particular, a spectacle lens. Moreover, a method for minimizing the difference in thickness between two ophthalmic lenses for the same spectacles is provided. A computer program product and a machine-readable storage medium are provided as well.

The invention claimed is: 
     
       1. A computer-implemented method for providing a lens shape for an ophthalmic lens, the method comprising:
 a) providing a predetermined lens shape of an ophthalmic lens having a front surface and a back surface, wherein the predetermined lens shape includes a predetermined shape of the front surface and a predetermined shape of the back surface within a prescription zone of the back surface bordered by a first boundary line, such that the ophthalmic lens satisfies predetermined optical properties within the prescription zone; 
 b) determining a carrier point on the back surface within the prescription zone and a plurality of carrier lines each extending from the carrier point into a respective direction; 
 c) determining a transition zone of the back surface, wherein the transition zone extends radially outwards from the first boundary line towards the outer edge of the ophthalmic lens and ends at a second boundary line bordering the transition zone radially outwards; 
 d) for each carrier line, setting a desired constant curvature gradient over the transition zone; 
 e) for each carrier line, determining a curvature profile of the back surface between the first boundary line and an outer edge of the ophthalmic lens along the carrier line, wherein the curvature profile in the transition zone is determined based on the respective desired constant curvature gradient; and 
 f) flattening a profile of the curvature of the prescription zone in the direction of the carrier lines along the first boundary line via approximation by a polynomial function, a spline function, or a Fourier series to obtain a flattened curvature profile and to provide for angular smoothing of the back surface radially outwards of the first boundary line, wherein the flattened curvature profile is set as a radially inward starting curvature value for each carrier line. 
 
     
     
       2. The method according to  claim 1 , wherein a curvature along the carrier line between the second boundary line and the outer edge is essentially constant and equals the curvature along the carrier line in the transition zone at the second boundary line. 
     
     
       3. The method according to  claim 1 , wherein the desired constant curvature gradient is set based on the curvature of the prescription zone at the first boundary line and a boundary condition for the curvature within the transition zone. 
     
     
       4. The method according to  claim 1 , wherein the desired constant curvature gradient is set based on the curvature of the prescription zone at the first boundary line and a curvature target to be reached at the second boundary line, and wherein the curvature target is at least one of zero or a curvature of the front surface. 
     
     
       5. The method according to  claim 1 , wherein the curvature gradient is set to be negative in case the ophthalmic lens is a minus lens and the curvature gradient is set to be positive in case the ophthalmic lens is a plus lens. 
     
     
       6. The method according to  claim 1 , wherein the curvature profile is determined by determining a cubic spline from the first boundary line to the second boundary line, wherein the cubic spline includes a plurality of sections each described by a cubic polynomial, and wherein the cubical polynomials are determined section-wise from the first boundary line to the second boundary line. 
     
     
       7. A computer-implemented method for providing a lens shape for an ophthalmic lens, the method comprising:
 a) providing a predetermined lens shape of an ophthalmic lens having a front surface and a back surface, wherein the predetermined lens shape includes a predetermined shape of the front surface and a predetermined shape of the back surface within a prescription zone of the back surface bordered by a first boundary line, such that the ophthalmic lens satisfies predetermined optical properties within the prescription zone; 
 b) determining a carrier point on the back surface within the prescription zone and a plurality of carrier lines each extending from the carrier point into a respective direction; 
 c) determining a transition zone of the back surface, wherein the transition zone extends radially outwards from the first boundary line towards the outer edge of the ophthalmic lens and ends at a second boundary line bordering the transition zone radially outwards; 
 d) for each carrier line, setting a desired constant curvature gradient over the transition zone: 
 e) for each carrier line, determining a curvature profile of the back surface between the first boundary line and an outer edge of the ophthalmic lens along the carrier line, wherein the curvature profile in the transition zone is determined based on the respective desired constant curvature gradient and 
 f) flattening a profile of the curvature of the prescription zone in the direction of the carrier lines along the first boundary line via approximation by a polynomial function, a spline function, or a Fourier series to obtain a flattened curvature profile and to provide for angular smoothing of the back surface radially outwards of the first boundary line, wherein the flattened curvature profile is set as a radially inward starting curvature value for each carrier line, 
 wherein the curvature profile is determined by determining a cubic spline from the first boundary line to the second boundary line, wherein the cubic spline includes a plurality of sections each described by a cubical polynomial, and wherein the cubical polynomials are determined section-wise from the first boundary line to the second boundary line such that a sagittal height, a slope, and a curvature of the back surface along the carrier line are continuous, and the curvature gradient is reset to the desired constant curvature gradient for each polynomial at the radially inwards end of each section. 
 
     
     
       8. The method of  claim 1 , wherein a length of the transition zone along each carrier line is constant, resulting in the second boundary line bordering the transition zone radially outwards, and the second boundary line being radially offset from the first boundary line by the length of the transition zone. 
     
     
       9. The method according to  claim 8 , wherein the length of the transition zone is within a range of at least 10 mm up to and including 20 mm. 
     
     
       10. The method according to  claim 1 , wherein the constant curvature gradient has a magnitude in a range of at least and including 0.05 diopters/mm up to and including 1.5 diopters/mm. 
     
     
       11. The method according to  claim 6 , wherein the length of each section is within a range of at least and including 0.5 mm up to and including 2 mm. 
     
     
       12. The method according to  claim 1 , wherein the method further comprises:
 checking, for each carrier line, whether a thickness of the ophthalmic lens at least at one of an outer edge or an intended frame line along which the ophthalmic lens is to be edged is above a predefined threshold and, if not, changing a magnitude of the desired constant curvature gradient. 
 
     
     
       13. The method according to  claim 1 , wherein the ophthalmic lens is an uncut finished spectacle lens. 
     
     
       14. The method according to  claim 1 , wherein a curvature profile of the predetermined lens shape of the back surface is preserved within the first boundary line. 
     
     
       15. The method according to  claim 1 , wherein at least a sagittal height of the prescription zone of the back surface transitions continuously at the first boundary line into each carrier line. 
     
     
       16. The method according to  claim 8 , wherein the length of the transition zone is measured within a tangential plane oriented tangentially to the carrier point of the back surface. 
     
     
       17. The method according to  claim 1 , wherein the carrier point is offset nasally from a prism reference point of the ophthalmic lens. 
     
     
       18. The method according to  claim 1 , wherein the first boundary line is circular and the second boundary line is circular. 
     
     
       19. The method according to  claim 1 , wherein the curvature profile along each carrier line radially outwards of the second boundary line is determined via a circular arc. 
     
     
       20. A computer-implemented method for providing a lens shape for an ophthalmic lens, the method comprising:
 a) providing a predetermined lens shape of an ophthalmic lens having a front surface and a back surface, wherein the predetermined lens shape includes a predetermined shape of the front surface and a predetermined shape of the back surface within a prescription zone of the back surface bordered by a first boundary line, such that the ophthalmic lens satisfies predetermined optical properties within the prescription zone; 
 b) determining a carrier point on the back surface within the prescription zone and a plurality of carrier lines each extending from the carrier point into a respective direction; 
 c) determining a transition zone of the back surface, wherein the transition zone extends radially outwards from the first boundary line towards the outer edge of the ophthalmic lens and ends at a second boundary line bordering the transition zone radially outwards; 
 d) for each carrier line, setting a desired constant curvature gradient over the transition zone; 
 e) for each carrier line, determining a curvature profile of the back surface between the first boundary line and an outer edge the ophthalmic lens along the carrier line, wherein the curvature profile in the transition zone is determined based on the respective desired constant curvature gradient; 
 f) providing an angular smoothing of the back surface radially outwards of the first boundary line by: 
 i) forming a series of coefficient values of corresponding coefficients of a respective function describing each carrier line in the transition zone, and 
 ii) determining, for each corresponding coefficient, a first Fourier series of a first order approximating the series of coefficient values, to obtain a first set of Fourier series each dependent on an angle around the carrier point, the first set of Fourier series describing any carrier line in a radial direction for a given angle. 
 
     
     
       21. The method according to  claim 20 , wherein the method further comprises:
 iii) determining, for each coefficient, a second Fourier series of a second order approximating the series of coefficient values, to obtain a second set of Fourier series each dependent on an angle around the carrier point, the second set of Fourier series describing any carrier line in a radial direction for the given angle, wherein the second order is higher than the first order, and wherein the second set of Fourier series is applied at the first boundary line, and 
 iv) blending the second set of Fourier series into the first set of Fourier series radially outwards over a blending zone. 
 
     
     
       22. A computer-implemented method for providing a lens shape for an ophthalmic lens, the method comprising:
 a) providing a predetermined lens shape of an ophthalmic lens having a front surface and a back surface, wherein the predetermined lens shape includes a predetermined shape of the front surface and a predetermined shape of the back surface within a prescription zone of the back surface bordered by a first boundary line, such that the ophthalmic lens satisfies predetermined optical properties within the prescription zone; 
 b) determining a carrier point on the back surface within the prescription zone and a plurality of carrier lines each extending from the carrier point into a respective direction; 
 c) determining a transition zone of the back surface, wherein the transition zone extends radially outwards from the first boundary line towards the outer edge of the ophthalmic lens and ends at a second boundary line bordering the transition zone radially outwards; 
 d) for each carrier line, setting a desired constant curvature gradient over the transition zone; 
 e) for each carrier line, determining a curvature profile of the back surface between the first boundary line and an outer edge the ophthalmic lens along the carrier line, wherein the curvature profile in the transition zone is determined based on the respective desired constant curvature gradient; 
 f) providing an angular smoothing of the back surface radially outwards of the first boundary line by: 
 i) forming a series of coefficient values of corresponding coefficients of a respective function describing each carrier line in the transition zone, 
 ii) determining, for each corresponding coefficient, a first Fourier series of a first order approximating the series of coefficient values, to obtain a first set of Fourier series each dependent on an angle around the carrier point, the first set of Fourier series describing any carrier line in a radial direction for a given angle, 
 iii) determining, for each coefficient, a second Fourier series of a second order approximating the series of coefficient values, to obtain a second set of Fourier series each dependent on an angle around the carrier point, the second set of Fourier series describing any carrier line in a radial direction for the given angle, wherein the second order is higher than the first order, and wherein the second set of Fourier series is applied at the first boundary line, and 
 iv) blending the second set of Fourier series into the first set of Fourier series radially outwards over a blending zone,
 wherein the step of blending is conducted via the following formula:
     Z=Z   2 ( A,R )+ W ( R )·( Z   1 ( A,R )− Z   2 ( A,R )),
 
 
 wherein Z is the resulting sagittal height, A is the angle around the carrier point, R is the radial distance from the carrier point, Z 1 (A,R) is the sagittal height at the angle A and the radial distance R based on the first set of Fourier series, and Z 2 (A,R) is the sagittal height at the angle and the radial distance based on the second set of Fourier series, and wherein W(R) is a quintic blending polynomial, with:
     w ( R )=10· t   3 −15· t   4 +6· t   5 ,
 
 
 wherein 
 
 
       
         
           
             
               
                 t 
                 = 
                 
                   
                     ( 
                     
                       R 
                       - 
                       
                         R 
                         ⁢ 
                         D 
                       
                     
                     ) 
                   
                   delta 
                 
               
               , 
             
           
         
       
       and wherein RD is the radial distance between the first boundary line and the carrier point at the angle A, wherein delta is the width of the blending zone, and wherein delta is 0.6 times the radial distance between the first boundary line and the carrier point at the angle A. 
     
     
       23. A method for constructing a surface determined by carrier lines radially outwards of a prescription zone of an ophthalmic lens, the method comprising:
 aa) providing a plurality of carrier lines each extending from a carrier point in the prescription zone into a respective direction, wherein a curvature profile of the surface along each carrier line radially outwards of the prescription zone is provided by a cubic spline; 
 bb) forming a first set of truncated Fourier series of a definite high order each approximating corresponding coefficients of a first spline for all carrier line directions, 
 cc) forming a second set of truncated Fourier series of a definite low order each approximating corresponding coefficients of a second spline for all carrier line directions, and 
 dd) determining a third spline sufficient to determine a surface height at any radial location within the range of the carrier lines for any specified carrier line direction by a weighted average of the first spline and second spline for that direction, where the weighting function is a polynomial function of the radial distance from a first boundary line. 
 
     
     
       24. A method for providing a surface determined by carrier lines radially outwards of a prescription zone of an ophthalmic lens, the prescription zone bordered by a first boundary line, the method comprising:
 i) providing a plurality of carrier lines each extending from a carrier point in the prescription zone into a respective direction, wherein a curvature profile of the surface in a direction along each carrier line radially outwards of the prescription zone has at least one section, wherein the curvature profiles of corresponding sections of each carrier line are provided by respective polynomials, 
 ii) forming a series of coefficient values of corresponding coefficients of the polynomials of each carrier line, 
 iii) determining, for each corresponding coefficient, a first Fourier series of a first order approximating the series of coefficient values, to obtain a first set of Fourier series each dependent on an angle around the carrier point, 
 iv) determining, for each coefficient, a second Fourier series of a second order approximating the series of coefficient values, to obtain a second set of Fourier series each dependent on an angle around the carrier point, the second set of Fourier series describing any carrier line in a radial direction for a given angle, wherein the second order is higher than the first order, and wherein the second set of Fourier series is applied at the first boundary line, and 
 v) blending the second set of Fourier series into the first set of Fourier series radially outwards over a blending zone, so that only the first set of Fourier series is applied beyond the blending zone. 
 
     
     
       25. The method according to  claim 24 , wherein the blending is conducted via the following formula:
     Z=Z   2 ( A,R )+ W ( R )·( Z   1 ( A,R )− Z   2 ( A,R )),
 
 
       wherein Z is the resulting sagittal height, A is the angle around the carrier point, R is the radial distance from the carrier point, Z 1 (A,R) is the sagittal height at the angle A and the radial distance R based on the first set of Fourier series, and Z 2 (A,R) is the sagittal height at the angle A and the radial distance R based on the second set of Fourier series, wherein W(R) is a quintic blending polynomial, wherein
     w ( R )=10· t   3 −15· t   4 +6· t   5 ,
 
 wherein 
 
       
         
           
             
               
                 t 
                 = 
                 
                   
                     ( 
                     
                       R 
                       - 
                       
                         R 
                         ⁢ 
                         D 
                       
                     
                     ) 
                   
                   delta 
                 
               
               , 
             
           
         
       
       wherein RD is the radial distance between the first boundary line and the carrier point at the angle A, wherein delta is the width of the blending zone, and wherein delta is 0.6 times radial distance between the first boundary line and the carrier point at the angle A. 
     
     
       26. A method for manufacturing an ophthalmic lens, the method comprising:
 providing a lens shape for an ophthalmic lens according to  claim 1 , and 
 manufacturing the ophthalmic lens according to the lens shape. 
 
     
     
       27. A computer program product stored on a non-transitory computer storage medium and comprising program code for carrying out the method according to  claim 1  when the computer program product is run on a data processing device. 
     
     
       28. A non-transitory, machine-readable storage medium having stored thereon a computer program comprising program code for carrying out the method according to  claim 1  when the computer program or the program code is run on a data processing device.